London (CNN) -- The Cabinet minister who oversees British broadcasting came under fire Tuesday after the inquiry into the News Corp. hacking scandal revealed extensive contacts with the company while he weighed a controversial merger.

Hundreds of pages of e-mails painted a picture of a back channel between Culture Secretary Jeremy Hunt and Frederic Michel, a top employee of James Murdoch, then head of News Corp.'s British newspaper operations. At the time, the company was seeking to take full control of satellite broadcaster BSkyB, and the documents suggest that News Corp. was getting inside information from Hunt, who had the power to block the acquisition.

In one January 2011 e-mail released Tuesday, Michel told Murdoch that he had gotten "absolutely illegal" information about government plans related to the takeover, which was scuttled by the hacking scandal.

Hunt is a member of Prime Minister David Cameron's Conservative party, and a top official of the Labour opposition called for his resignation after Tuesday's disclosures. Harriet Harman, Labour's deputy leader and the party's "shadow secretary" for culture, media and sport, issued the call in the House of Commons.

But Cameron has full confidence in Hunt, whose portfolio includes the upcoming Olympic Games in London, Downing Street spokesman Craig Oliver said. And in a statement issued after the meeting, Hunt said he has asked for his appearance before the Leveson Inquiry to be moved up "to resolve this issue as soon as possible."

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"Now is not a time for knee-jerk reactions. We've heard one side of the story today, but some of the evidence reported meetings and conversations that simply didn't happen," he said.

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"I am very confident that when I present my evidence the public will see that I conducted this process with scrupulous fairness," he added.

Numerous e-mails from Michel, News Corp.'s public affairs director for Europe, recount his talks with Hunt over the planned takeover. In one, Michel advises Murdoch that he has details of an upcoming statement on the merger to Parliament "although absolutely illegal."

"He said that the key for us tomorrow was to be able to sustain the heat around Ofcom" -- the independent regulator for the British communications industry -- "recommending a referral and making sure we put our arguments from the submissions out," Michel wrote in January 2011.

That March, Michel reported that Hunt asked to be kept informed of News Corp. discussions with the government's Office of Fair Trading "so he can push them if needed." And in April, with the phone-hacking scandal flaring up, he advised Murdoch that it wouldn't affect the BSkyB deal -- but said the company was pushing the government to announce a decision "as early as possible."

Murdoch, the son of News Corp. chief Rupert Murdoch, defended the company's contacts with Hunt during his Tuesday appearance before the Leveson Inquiry. Murdoch told the inquiry that there was no "quid pro quo" with political figures who could advance the company's business interests.

"The question of support for an individual newspaper for politicians one way or another is not something that I would ever link to a commercial transaction like this," he said. "Nor would I expect that political support one way or another to ever translate into a minister behaving in an inappropriate way, ever. I would never do business that way."

Murdoch's biggest paper, the Sun, endorsed Cameron's Conservatives in the 2010 election that brought them to power. But he said Hunt followed the advice of independent regulators "at every single decision point" in the BSkyB review.

Murdoch also told the inquiry that he had had drinks with Cameron at a pub before he became prime minister and dined with him once he was in office. He was also pressed on his relationship with other British politicians, including former Prime Minister Tony Blair, and he denied having lobbied them improperly about his family's business interests.